Mathematics Education at the University: An
Item Difficult to Enter on. The difficulties are: high deficiency
of mathematical knowledge that new students bring from high school and
absence of motivation and lack of training of the students for problem
solving. To solve these problems a research group on mathematics
education at the School of Biochemistry designed a distance education
course. This course is written with an historical view and based in the
heuristic methodology. Since motivation is very important, they looked
for problems intimately connected with the discipline chosen. The visual
impact plays important roles in motivation because sensitive experiences
are the background upon which deeper knowledge is built. Finally, the
problem solving is the methodology with which we are working. The
resolution of mathematical problems supplies students with techniques,
which can be used in different areas, even to everyday problems.
Mathematical thinking is logical and strict, intuitive and creative,
dynamic and changing.

The
Preparation Needs of New Graduate Teaching Assistants. In the
USA, Graduate Teaching Assistants (GTAs, both domestic and international)
are critical in the effective mathematics education of undergraduates
because they teach a large percentage of lower division courses. A variety
of efforts have been implemented to prepare these instructors to teach in
a variety of ways with a diversity of students and an evolving curriculum,
a context which is often different from the one in which GTAs learned
mathematics. The joint Committee on Teaching Assistants and Part-Time
Instructors of the American Mathematical Society (AMS) and the
Mathematical Association of America (MAA) has held sessions at national
conferences in order to explore this issue. I will present: (1) an
analysis of themes and emerging ideas from the AMS/MAA sessions and (2)
results from an in-depth study of 25 new GTAs at the University of
Oklahoma. This latter project will examine the perspective of new GTAs,
using journal entries, statements of teaching philosophy, and videotapes
of classroom teaching as data.

Four Clues to Teaching Mathematics: Good or Right and Complexity or
Abstraction. In studying mathematics two types of attitude are
required; one acceptance or agreement and the other argument.
Definitions and notations are important in mathematics and they are
something that is adopted. They are essentially matters of good or bad.
On the other hand another important part of mathematics is logical
argument. Logical argument is essentially a matter of right or wrong,
not good or bad. Many students tend to have interchanged attitudes in
this aspect. I believe that their wrong attitudes make their study of
mathematics harder. If we take these attitudes as warp, there are two
types of difficulties of mathematics as woof: one the difficulty due to
complexity, the other due to abstraction. Abstraction is harder to
conceive and rather unfamiliar to everyone, and thus requires extra work
for it. I believe that if instructors indicate the nature of the
difficulty according to these four clues it would increase the
effectiveness of teaching mathematics.

The Genetic Principle in Teaching University Mathematics. The
genetic approach in mathematics teaching has been known from the times of
Diesterweg, but it was almost never used in teaching higher mathematics:
it was assumed that for undergraduate students, mathematics should be
taught in strict logical and deductive way. For example, the teaching of
mathematical disciplines in universities began with detailed account of
logical and set-theoretic foundations, the linear algebra courses began
with the general theory of vector spaces etc. However, modern experience
has shown that the strict logical and deductive teaching of mathematics
is inappropriate for undergraduate mathematics teaching, too. This
presentation discusses the genetic approach to teaching higher
mathematics. This approach consists in presenting subject matter as
developing out of the principles that have determined its presented form.
Such approach requires, for example, that elements of number theory
should be taught before abstract algebra.

Statistical Literacy: A Pre-Stats Bridging Course. The
traditional applied statistics course is not accomplishing its mission.
It has too many topics and does not do enough in helping students
evaluate non-statistical arguments involving statistics. This paper
argues that there are two causes. First, an over-emphasis on statistical
inference -- on chance, sampling distributions, confidence intervals and
hypothesis tests. Second, an under-emphasis on statistical literacy: the
distinction between association and causation, between experiments and
observational studies, between a biased measurement and a spurious
association, between a frequentist p-value and a Bayesian strength of
belief. Since both statistical inference and statistical literacy are
extremely important, this paper proposes a new course: a "Statistical
Literacy" bridging course. This is not a "baby stats" course; it is not
just a vocational remediation course that reviews arithmetic and algebra.
Instead, this is a critical thinking course that focuses on descriptive
statistics and modeling with a strong emphasis on conditional thinking
and on written communication using proper English.